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İnsan Tunalı Econ 320: Labor Economics 27 April 2017 Answers to Assignment 9 Problems from Borjas, Ch.7 7-2. What effect will each of the following proposed changes have on wage inequality? (a) Indexing the minimum wage to inflation. Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage helps prop up the wages of less skilled workers. Note that an increase in the minimum wage may have negative employment effects, but the proposed policy is not to increase the minimum wage but rather simply to prevent it from falling in real terms. (b) Increasing the benefit level paid to welfare recipients. Wage inequality measures the dispersion of wages in the working population. An increase in welfare benefits would likely induce less-skilled workers out of the labor force, and would reduce measured wage inequality by effectively eliminating the bottom of the wage distribution. (c) Increasing wage subsidies paid to firms that hire low-skill workers. Wage subsidies would increase the demand for less skilled workers, reducing wage inequality. 7-3. From 1970 to 2000, the supply of college graduates to the labor market increased dramatically, while the supply of high school (no college) graduates shrunk. At the same time, the average real wage of college graduates stayed relatively stable, while the average real wage of high school graduates fell. How can these wage patterns be explained? The graphs below show equilibrium movements in the market for high school graduates and in the market for college graduates. The decrease in labor supply among high school graduates and the increase in labor supply among college graduates is taken as given. The analysis, therefore, focuses on labor demand for each type of labor. Given a lower supply of high school graduates, the only way for their average wage to fall is for labor demand for high school graduates to have decreased (shifted in). Labor Market for High School Graduates LS2000 LS1970 w1970 w2000 LD1970 LD2000 L2000 L1970 Given a greater supply of college graduates, the only way for their average wage to stay the same is for labor demand for college graduates to have increased (shifted out). Labor Market for College Graduates LD1970 LS1970 LS2000 LD2000 w1970 = w2000 L1970 L2000 7-4. (a) Is the presence of an underground economy likely to result in a Gini coefficient that overstates or under-states poverty? The larger the underground economy, the more the Gini coefficient is likely to over-state poverty as the underground economy tends to employ low-skill, low-income workers. (b) Consider a simple economy where 90 percent of citizens report an annual income of $10,000 while the remaining 10 percent report an annual income of $110,000. What is the Gini coefficient associated with this economy? As all citizens in each group receive an equal income, the actual Lorenz curve will be a straight line within each group. Let’s suppose there are 1,000 citizens. The 90% of poorest citizens, therefore, receive 0.90 x 1000 x $10,000 = $9 million. The entire economy, though, earns 0.9(10,000)+0.1(110,000) = $20 million. Therefore, the bottom 90% receives 9 ÷ 20 = 45% of total income. The perfect and actual Lorenz curves can now be drawn rather easily. Share of Income 1.00 Perfect-Equality Lorenz Curve Actual Lorenz Curve 0.45 0.00 0 0.9 Share of Citizens 1.00 The Gini coefficient is now easily calculated by seeing that the area beneath the actual Lorenz curve is two triangles and one rectangle. Gini = (1 / 2) − [(1 / 2)(0.9)(0.45) + (0.1)(0.45) + (1 / 2)(0.1)(0.55)] = 0.45 . (1 / 2) 2 (c) Suppose the poorest 90 percent of citizens actually have an income of $15,000 because each receives $5,000 of unreported income from the underground economy. What is the Gini coefficient now? The problem is identical to that above, but the income levels change. In this case, per capita GDP is 0.9 x 15,000 + 0.1 x 110,000 = $24,500 so total income of the 1,000 citizens is $24,500,000. Lastly, the total income share of the poorest 90% of citizens is 900 x 15000 ÷ 24.5 million = 55.1%. (That is, in the graph on the previous page, the income share at 90% of citizens increases from 45% to 55.1%.) The Gini coefficient is not calculated as it was before: Gini = (1 / 2) − [(1 / 2)(0.9)(0.551) + (0.1)(0.551) + (1 / 2)(0.1)(0.449)] = 0.349 (1 / 2) 7-10. Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 – 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200 – 0.2Q. Ms. Aura’s operation has no fixed costs, but she incurs a cost of $150 per session (going to the client’s house). (a) What is Ms. Aura’s yearly profit? Find the number of sessions that Ms. Aura will provide by equating the marginal revenue to the marginal cost of a session: setting MR = MC yields 200 – 0.2Q = 150 which solves as Q* = 250. The price that would generate demand for 250 sessions is $175 as 2,000 – 10(175) = 250. Thus, her annual profit is 175(250) – 150(250) = $6,250 per year. (b) Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500 – 5P. Her new marginal revenue is MR = 500 – 0.4Q. What is her profit now? The same kind of calculations as in part (a) but using the new demand curve yields a profit maximizing quantity of 875 sessions at $325 per session and an annual profit of $153,125. (c) Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of $1,000, but the marginal cost is only $20 per session. What is Ms. Aura’s profit? Assume the demand curve is still given by Q = 2500 – 5P. With the new marginal cost, Ms. Aura will provide 1,200 sessions and charge $260 per session. Her annual profit will equal $287,000. (d) Summarize the lesson of this problem for the superstar phenomenon. Borjas: Superstars command an economic rent because they are, in essence, a monopoly with a favorable demand curve. The greater the demand for the superstar’s product, the higher price the superstar can charge, and the more profit can be earned. Notice also that, going from part (a) to part (b), is the lesson that when demand for your services is high, you provide a lot of service, i.e., an upward sloping labor supply curve. Two excellent answers from last Econ 320: Emre: First of all, due to being famous, the demand and price of the [service] rises drastically. In addition, this drastic increase of demand and price is not followed by an increase of marginal costs or does not face supply limitations. Also, technological advancements decrease costs and also increase potential supply. Therefore … .she is able to sell to a much wider group… does not have … time constraint due to the nature of the product and also due to technology; while being able to sell the good at much higher prices because of the fame. 3 Cem: Since all fortune tellers are not easily substitutable (and since we are willing to pay a lot more for an accurate guess about our future) and their talents can be sold to large crowds with telecommunication we can see that [while] … fortune tellers with less abilities earn significantly less, their famous counterparts [earn quite a bit more]. Part II. Old Exam Question The table below is based on data collected by the Household Budget Survey conducted in Turkey in 2005. Household Income Per capita Income Share of Income Cumulative Share of Income Share of Income Cumulative Share of Income First 20% 6.0 6.0 6.0 6.0 Second 20% 11.2 17.2 12.0 18.0 Third 20% 15.8 33.0 16.1 34.1 Fourth 20% 22.6 55.6 22.2 56.3 Fifth 20% 44.4 100.0 43.7 100.0 Quintiles 1. Use a graph to sketch the Lorenz curve for Household Income. Mark the axes. Lorenz curve = Cumulative Share of Income as a function of quintiles. Lorenz Curve for Household Income Share of income 1 0,8 0,6 0,4 0,2 0 0 0,2 0,4 0,6 Share of households Perfect Equality Lorenz Curve (45 degree) 0,8 1 Actual Lorenz Curve 2. Use your graph to illustrate how the Gini coefficient is calculated. Explain what the Gini coefficient measures. Let A = Area between the 45 degree line and the Lorenz curve, and A + B denote the area of the triangle. Then G = Gini coefficient = A/(A + B). It measures the degree of inequality. By construction 0 < G < 1. 4 3. Consider the Per capita Income distribution shown in the table. Is that distribution more, or less equal than Household Income distribution? Defend your answer. More equal, because the Cum. Share of Per Capita Income ≥ the Cum. Share of HH Income at every quintile. Lorenz Curves (LCs) 1 0,9 Share of income 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0 0,2 0,4 0,6 0,8 Share of households/individuals 1 Perf ect Equality Lorenz Curve (45 degree) LC f or household income LC f or per capita income 4. Use a separate graph to sketch a log-normal earnings distribution. Is this distribution consistent with the income distribution data from Turkey? From the USA? A log-normal earnings distribution is left-skewed (has a long right tail). For the data from Turkey shown in class, “log-normal” appears to be a good description. See below. Daily earnings in Turkey (TLx1000), 1988 Fraction .2 .1 0 0 10 20 30 gucrety See Borjas, Figure 7-1 for the U.S. version. (Statistical definition: A random variable W has the log-normal distribution if log-W has a normal distribution.) 5. Why does the typical earnings distribution have a long right tail? Discuss. Higher ability people are more likely to invest in higher levels of education, and post-school investments are higher at higher levels of education. Both of these factors result in a distribution which is skewed to the right. Also, the superstar phenomenon (whereby a handful of famous people dominate the pay scales in every field) and tournament model (or other incentive based) pay scales stretch the right tail further. 5